The generator matrix 1 0 0 0 0 0 0 0 1 1 1 X 1 1 0 1 0 X 1 X 0 1 X 1 1 0 0 1 X X 1 0 1 X 1 X 1 0 X 1 X X X 1 0 1 1 X X 1 1 1 1 1 1 1 1 X 1 X X 1 1 1 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X X X X X X X X 1 1 1 1 1 1 X+1 1 1 1 1 1 1 1 1 1 1 X+1 X X+1 1 X 1 1 1 X 0 X X X+1 X 1 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 X 1 1 1 1 X+1 1 1 1 X X+1 X 0 0 1 1 1 X+1 1 X+1 1 X 1 X+1 X+1 0 X X+1 X+1 0 X+1 1 X+1 X+1 X 0 0 0 X X X+1 X X+1 X 0 1 0 1 X+1 X+1 X 1 X+1 X X+1 0 0 0 0 1 0 0 0 0 0 1 X 1 0 1 X 0 1 1 1 X+1 1 X+1 0 X 1 X 1 X+1 X X X 0 X 0 0 X+1 0 X 0 X+1 X+1 X+1 X 1 0 1 X+1 0 1 1 1 0 X X+1 1 1 0 0 0 1 X 1 0 1 0 0 X X+1 0 0 0 0 0 1 0 0 0 1 0 1 1 X X+1 1 X X+1 0 X X X+1 1 X X 0 1 X 1 X X+1 0 0 X+1 0 1 X+1 1 1 1 0 X+1 0 X+1 1 0 1 X 0 X+1 1 X X+1 1 X X+1 X+1 0 1 X X+1 X X+1 X+1 X 0 X 1 X 0 0 0 0 0 0 1 0 0 1 X 0 X+1 1 1 1 0 X 1 1 1 X+1 0 1 X+1 X+1 X 1 X 1 X 0 1 X+1 0 X 1 0 0 X+1 1 1 0 1 X X X 0 0 X+1 0 X 0 0 0 0 X+1 1 X+1 1 X+1 X+1 0 0 X+1 X X 0 1 0 0 0 0 0 0 0 1 0 1 X+1 X+1 1 X+1 0 X 0 0 1 1 X X+1 X X+1 0 1 X+1 0 X+1 X+1 X 1 0 0 1 X+1 1 X+1 X+1 X 1 X 0 1 X X 1 0 X+1 0 0 X X X 1 0 1 0 1 X 1 X X X 1 0 0 X+1 0 0 0 0 0 0 0 0 0 1 X X 1 1 1 1 1 X+1 X+1 X+1 0 0 0 X X 0 1 1 1 X+1 X+1 X 0 X+1 X X X 1 X+1 X 0 0 X 0 0 0 X+1 X 0 X+1 1 X+1 X+1 1 1 X+1 0 0 1 X+1 X+1 X+1 1 1 0 0 X X X X 1 generates a code of length 69 over Z2[X]/(X^2) who´s minimum homogenous weight is 53. Homogenous weight enumerator: w(x)=1x^0+34x^53+145x^54+296x^55+456x^56+724x^57+932x^58+1186x^59+1539x^60+1790x^61+2168x^62+2658x^63+2884x^64+3238x^65+3853x^66+4048x^67+4267x^68+4446x^69+4271x^70+4156x^71+3986x^72+3780x^73+3282x^74+2676x^75+2231x^76+1754x^77+1428x^78+1042x^79+733x^80+518x^81+353x^82+264x^83+129x^84+88x^85+66x^86+56x^87+28x^88+12x^89+12x^90+2x^91+2x^92+2x^94 The gray image is a linear code over GF(2) with n=138, k=16 and d=53. This code was found by Heurico 1.11 in 237 seconds.